The hunt for the new Royal Bank of Scotland Group PLC chief executive is heating up, but one of the favorites for the politically-charged role has now dropped out.

RBS is hoping to unveil its new chief executive next week when the bank announces first half results, according to people close to the process. The bank has drawn up a shortlist of two internal and two external candidates, one person said.

Now, one tipped external candidate, Mark McCombe, who heads the Asia operations of fund manager BlackRock Inc., has ruled himself out of the process. Mr. McCombe sent an email to his senior team yesterday saying that he had been contacted about the job but wanted to stay at BlackRock, according to a person familiar with the email. Mr.McCombe was not made available to comment.

Internal candidates include RBS’s newly appointed head of retail banking Ross McEwan, according to a person familiar with the process. Mr. McEwan joined the bank in 2012 from Commonwealth Bank of Australia. As RBS continues to boil down its investment bank and refocus on its retail business, his expertise could be in demand, analysts say. However the New Zealand born executive is new to Britain and will have to navigate the highly political job — RBS is still 81% owned by the U.K. government.

Current CEO Stephen Hester announced he would step down at the end of the year, helping ensure a smooth transition. His successor will have to pledge to stay for at least five years to follow through with the bank’s privatization. Finding a suitable candidate is further complicated by the fact that the bank can only be seen to hand out a moderate pay package. The executive in question will also have to stand up to intense media scrutiny, a problem for any seasoned candidate who took part in pre-crisis excesses.

Anna Mann, founder of MWM Consulting, is leading the search. MWM didn’t return calls for comment or make Ms. Mann available.